Find the equation of the tangent and the normal to the following curves at the indicated points:
$y^{2}=4 a \times a t\left(a / m^{2}, 2 a / m\right)$
finding the slope of the tangent by differentiating the curve
$2 y \frac{d y}{d x}=4 a$
$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{2 \mathrm{a}}{\mathrm{y}}$
$\mathrm{m}$ (tangent) at $\left(\frac{\mathrm{a}}{\mathrm{m}^{2}}, \frac{2 \mathrm{a}}{\mathrm{m}}\right)$
$\mathrm{m}$ (tangent) $=\mathrm{m}$
normal is perpendicular to tangent so, $m_{1} m_{2}=-1$
$\mathrm{m}$ (normal) $=-\frac{1}{\mathrm{~m}}$
equation of tangent is given by $y-y_{1}=m($ tangent $)\left(x-x_{1}\right)$
$\mathrm{y}-\frac{2 \mathrm{a}}{\mathrm{m}}=\mathrm{m}\left(\mathrm{x}-\frac{\mathrm{a}}{\mathrm{m}^{2}}\right)$
equation of normal is given by $y-y_{1}=m($ normal $)\left(x-x_{1}\right)$
$y-\frac{2 a}{m}=-\frac{1}{m}\left(x-\frac{a}{m^{2}}\right)$